Hydrodynamic Simulations in 3+1 General Relativity

TL;DR

This paper presents a new computational scheme for simulating astrophysical systems involving strong gravity, such as neutron stars and black hole formation, using 3+1 general relativity coupled with relativistic hydrodynamics.

Contribution

It introduces novel techniques for evolving Einstein-hydrodynamics equations without artificial atmospheres and demonstrates their effectiveness in complex scenarios.

Findings

Successfully simulated collapsing rotating stars to black holes.

Evolved binary neutron star systems in quasi-equilibrium for over two orbits.

Identified superior gauge choices for lapse and shift in simulations.

Abstract

We solve Einstein's field equations coupled to relativistic hydrodynamics in full 3+1 general relativity to evolve astrophysical systems characterized by strong gravitational fields. We model rotating, collapsing and binary stars by idealized polytropic equations of state, with neutron stars as the main application. Our scheme is based on the BSSN formulation of the field equations. We assume adiabatic flow, but allow for the formation of shocks. We determine the appearance of black holes by means of an apparent horizon finder. We introduce several new techniques for integrating the coupled Einstein-hydrodynamics system. For example, we choose our fluid variables so that they can be evolved without employing an artificial atmosphere. We also demonstrate the utility of working in a rotating coordinate system for some problems. We use rotating stars to experiment with several gauge choices for the lapse function and shift vector, and find some choices to be superior to others. We demonstrate the ability of our code to follow a rotating star that collapses from large radius to a black hole. Finally, we exploit rotating coordinates to evolve a corotating binary neutron star system in a quasi-equilibrium circular orbit for more than two orbital periods.